From Wiki ... yes/no ...
"Federal military personnel have a long history of domestic roles, including the occupation of secessionist Southern states during Reconstruction. The Posse Comitatus Act prohibits the use of federal military personnel to "execute the laws"; however, there is disagreement over whether this language may apply to troops used in an advisory, support, disaster response, or other homeland defense role, as opposed to domestic law enforcement.
On March 10, 2009, members of the U.S. Army Military Police Corps from Fort Rucker were deployed to Samson, Alabama, in response to a murder spree. Samson officials confirmed that the soldiers assisted in traffic control and securing the crime scene. The governor of Alabama did not request military assistance nor did President Obama authorize their deployment. Subsequent investigation found that the Posse Comitatus Act was violated and several military members received "administrative actions"."
So it depends in which capacity they are used, and depending on what a judge thinks. The last example is clear, because while the governor didn't authorize it, neither did the President. But if a governor didn't authorize it, but a President did ... I see no problem. That may happen in California shortly. My original point being ... this was originally envisaged as part of States Rights, and governors as mini-CnC ... which is where the call-up of Confederate troops came from. That will not be allowed to happen again. De facto, the National Guard is federalized, otherwise the Civil Rights enforcements of the 1960s couldn't have happened, since no Southern governor would have authorized it.